Treflan (Trifluralin) is a pre emergent herbicide. That means it prevents seeds from germinating and that includes vegetable seeds. It also has a residual that may cause difficulty with vegetable seed germination in the future.

Remember that herbicides like these do nothing to control established weeds they only prevent seed germination. 

The bottom line is that I don't think it would be a good idea to use Treflan on your vegetable garden. 

You can treat with Treflan and then plant sets and they will be OK, but again if you are doing crop rotation you might wind up with troubles in the future. 

You might want to look into some alternatives for weed control. Here is a good article from the U on controlling weeds in the home garden:Controlling weeds in home gardens | UMN Extension.

I have seen articles that it is OK to apply Treflan or Preen after the vegetables have germinated, but by then it might be too late as the weed seeds may have already germinated. There is a Preen product for vegetable gardens that is based on corn gluten rather than Trifluralin.

I haven't seen a comprehensive cheat sheet of what herbicides should be used with what crop. All Herbicide labels list what vegetable crops they can be used on and you may have to do a little research. Try searching for "herbicides for use on Strawberries" or "herbicides for use on raspberries" and you will get some options.

Hope this gives you some ideas. If you have more questions just respond to this answer and I will get the questioin.